This tea pet is in the likeness of Bodhidharma, the Indian priest who brought the Buddhist Dharma to China. The first patriarch of Chan (aka Zen) Buddhism, Bodhidharma had a profound impact on the development of both Buddhism and East Asian civilization. He is also closely associated with tea - one creation myth purports that the first two tea plants emerged from Bodhidharma's amputated eyelids, which he tore off in frustration when he kept falling asleep during meditation. This, says the legend, is why tea leaves are the shape of eyelids, and why they help you stay awake.
Chan monks performed a ritual before meditation honoring Bodhidharma, whereby they would share a bowl of tea with the patriarch symbolically by bowing to his portrait as they drink tea. This was the origin of the Buddhist tea ceremony that later gave rise to the Japanese tea ceremony.
This Bodhidharma has intact eyelids which are closed in deep meditation. His body dovetails seamlessly into a piece of wood, a reference to the concept of "deadwood Chan/Zen", where the body becomes inert as dead wood as the mind becomes more and more focused on itself. Pouring tea on Bodhidharma evokes meditation, devotion, the Buddha, and Buddhism, especially Chan/Zen.
Tea pets 茶寵 (Chá Chǒng) are small figurines, usually made of unglazed stoneware (such as the kind teapots are made from), in the shape of animals, people, gods, mythical beasts, plants, fungi - pretty much anything at all. Their sole purpose is to be a recipient of waste water and waste tea produced over the course of the tea service from heating and rinsing the wares and leaves. Over time, they develop a patina of tea oils the way that tea pots do. This process of "raising" as it is called allows them to develop a dark, shiny lustre, with each tea pet taking on its own look and personality over time with use. They also serve a votive function - the pouring of tea over the figure calls in the "spirit" of whatever that figure represents. A good tea pet looks best when in use - ie when enjoying a stream of hot tea being poured over it.